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Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-003128
EDN: 
FDJOOM

Multistability of synchronous modes in a multimachine power grid with a common load and their global and non-local stability

Autors: 
Khramenkov Vladislav Anatolevich, Institute of Applied Physics of the Russian Academy of Sciences
Dmitrichev Aleksej Sergeevich, Institute of Applied Physics of the Russian Academy of Sciences
Nekorkin Vladimir Isaakovich, Institute of Applied Physics of the Russian Academy of Sciences
Abstract: 

The purpose of this work is studying the dynamics of the power grid consisting of an arbitrary number of synchronous generators supplying a common passive linear load. We focus on searching the conditions for the existence and stability of synchronous modes, i.e. the main operating modes of a power grid. The possibility of the existence of non-synchronous (quasi-synchronous and asynchronous) modes is investigated.

Methods. To study the dynamics of a power grid we use the effective network model in the form of an ensemble of globally coupled nodes-generators. The state of every node is described by the swing equation. The approach for reducing the effective network to the network with a hub topology (star topology) is proposed. We use numerical methods to construct a partition of the parameter space into areas with different operating modes of the power grid.

Results. The conditions for the existence, stability and multistability of synchronous modes are obtained. The main characteristics of these modes are considered, such as the power supplied by generators to the grid and the distribution of currents along transmission lines. We constructed the partition of the power gird parameter space into areas with different dynamics.

Conclusion. The power grid consisting of an arbitrary number of synchronous generators supplying a common passive linear load has been studied. We shown the presence of two types of synchronous modes: homogeneous and inhomogeneous. The first is characterized by equal powers and currents flowing through all load supply paths except one. The second provides another additional path, which differs from the others in current and transmitted power. Moreover, the currents flowing along the same path, but in various modes, differ. The presence of high multistability of inhomogeneous synchronous modes has been established. The possibility of coexistence of homogeneous and inhomogeneous synchronous modes, as well as quasi-synchronous and asynchronous modes, is shown. In the power grid parameters space we found areas corresponding both the existence of only synchronous modes and their coexistence with quasi-synchronous and/or asynchronous modes.
 

Key words: 
power grids
synchronous machines
synchronous modes
global and non-local stability
multistability
Acknowledgments: 
The development of a model of a multi-machine power grid with a common load and a method for reduction of the power grid (section 1, Appendix), as well as the analysis of synchronous modes (section 2), were carried out with the support of the Russian Science Foundation, project No. 24-12-00245. The numerical study of non-synchronous modes of the power grid (section 3) was supported by the project No. 075-02-2024-1376 of Program for the Development of the Regional Scientific and Educational Mathematical Center “Mathematics of Future Technologies”.
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Received: 
06.06.2024
Accepted: 
11.07.2024
Available online: 
16.10.2024
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